The present invention relates to a quantum computer.
Quantum information processing covers a variety of fields where quantum mechanical effects are used to process information in applications such as computation and communications. An introduction to this subject is found in xe2x80x9cIntroduction to Quantum Computation and Informationxe2x80x9d ed. Hoi-Kwong Lo, Tim Spiller and Sandu Popescu (World Scientific Publishing, 1998).
Quantum computation involves manipulation of data in form of quantum bits or xe2x80x9cqubitsxe2x80x9d. Whereas in classical computation a bit of information is used to represent only one of two possible logical states, namely xe2x80x9c1xe2x80x9d or xe2x80x9c0xe2x80x9d, in quantum computation, a qubit can represent both logical states simultaneously as a superposition of quantum states. This property gives rise to powerful computational parallelism. Algorithms which exploit this parallelism have been developed, for example, for efficiently factorising large integers. An overview of quantum computing is found in xe2x80x9cQuantum Computationxe2x80x9d by David Deutsh and Artur Ekert in Physics World, pp. 47-52, March 1998 and in xe2x80x9cQuantum Computation: An Introductionxe2x80x9d by Adriano Barenco, pp. 143-183 of xe2x80x9cIntroduction to Quantum Computation and Informationxe2x80x9d ibid.
In known systems, a qubit is stored using left and right polarisation states of a photon, spin-up and spin-down states of an electron and ground and excited states of a quantum dot.
The qubit is defined by a basis consisting of two states, which are denoted |0 greater than  and |1 greater than . Thus, the state of the qubit can be represented as:
|"psgr" greater than =a|0 greater than +b|1 greater than 
where a and b are complex number coefficients. The qubit can store information as a combination of 0 and 1, using different values of a and b. However, a measurement of the qubit will cause it to project onto |0 greater than  or |1 greater than  state and return the result 0 or 1 respectively. The probabilities of returning these values are |a|2 and |b|2 respectively. In this way, a system comprised of one qubit can store two binary values, 0 and 1, at the same time, although recovery of any stored information is restricted.
A system comprised of two qubits can store up to four binary values simultaneously as a result of superposition. A system comprising a pair of qubits, labelled A and B, is defined by a basis of four states which can be written as |0 greater than A|0 greater than B, |0 greater than A|1 greater than B, |1 greater than A|0 greater than B and |1 greater than A|1 greater than B. In the same way a single qubit can store information as a superposition of |0 greater than  and |1 greater than , a pair of qubits can store information as a superposition of the basis states |0 greater than A|0 greater than B, |0 greater than A|1 greater than B, |1 greater than A|0 greater than B and |1 greater than A|1 greater than B. For example, the two qubits may be prepared such that:
|"psgr" greater than AB=2xe2x88x92xc2xd(|0 greater than A|0 greater than B+|0 greater than A|1 greater than B+|1 greater than A|0 greater than B+|1 greater than A|1 greater than B) 
Thus, four binary values 00, 01, 10 and 11 are encoded simultaneously. In this case, the two qubits exist independently of one another, such that the result of a measurement of qubit A is independent of the result of a measurement of qubit B.
However, if the two qubits are entangled, then the two measurements will become correlated. Entanglement allows qubits to be prepared such that:
|"psgr" greater than AB=2xe2x88x92xc2xd(|0 greater than A|0 greater than B+|1 greater than A|1 greater than B) 
Thus, binary values 00 and 11 are encoded simultaneously. However, if qubit A is measured and a result 0 is returned, then the outcome of a subsequent measurement of qubit B will, with certainty, also be 0.
A system comprised of three qubits is defined by a basis of eight states which can store eight binary numbers, 000, 001, . . . , 111 simultaneously.
In general, a system of m qubits has a basis of 2m states and can be used to represent numbers from 0 to 2mxe2x88x921. Thus, a quantum computer has a clear advantage over its classical counterpart in that it that it can store 2m numbers simultaneously, whereas a classical computer with an m-bit input register can only store one of these numbers at a time.
It is the ability to store many numbers simultaneously using superposition of quantum states which makes quantum parallel processing possible. Using a single computational step it is possible to perform the same mathematical operation on 2m different numbers at the same time and produce a superposition of corresponding output states. To achieve the same result in a classical computer, the computational step would need to be repeated 2m times or require 2m different processors.
Despite the power of quantum parallel processing, there is a drawback that only one state can be measured. However, some processes, such as sorting or searching a database, may require only a single-valued solution. Thus, a system in which a mathematical operation has been performed on a plurality of numbers simultaneously may still benefit from parallelism provided that the desired value is the most probable outcome when the system is measured. An example of a quantum algorithm which operates in this way is described in xe2x80x9cA Fast Quantum Mechanical Algorithm for Database Searchxe2x80x9d by Lov Grover, pp. 212-219, Proceedings of the 28th Annual ACM Symposium on the Theory of Computing (Philadelphia, May 1996).
So far, experimental quantum computers have been implemented using atomic beams, trapped ions and bulk nuclear magnetic resonance. Examples of these systems are described in xe2x80x9cQuantum computers, Error-Correction and Networking: Quantum Optical approachesxe2x80x9d by Thomas Pellizari, pp. 270-310 and xe2x80x9cQuantum Computation with Nuclear Magnetic Resonancexe2x80x9d by Isaac Chuang pp. 311-339 of xe2x80x9cIntroduction to Quantum Computation and Informationxe2x80x9d ibid. However, these systems have the disadvantage that their architecture cannot be easily scaled to accommodate large number of qubits, i.e. more than about 10 qubits.
Quantum computers may also be implemented using solid-state systems employing semiconductor nanostructures and Josephson junctions. One such device is described in xe2x80x9cCoherent control of macroscopic quantum states in a single-Cooper-pair boxxe2x80x9d by Y. Nakamura, Yu. A. Pashkin and J. S. Tsai, Nature, volume 398, p 786 (1999). The advantage of such solid state systems is that they ate better suited to being scaled and so provide quantum computers of practical utility.
A generally recognised problem is that quantum computation, and indeed any systems involving sensitive information processing, requires a quiet electromagnetic environment to operate. If the system interacts with the environment, then it loses coherence and quantum parallelism is destroyed.
The present invention seeks to provide a quantum computer and a device for providing a quiet electromagnetic environment.
According to a first aspect of the present invention there is provided a quantum computer for transforming a first state into a second state comprising a first quantum dot, a second quantum dot, said first and second quantum dots being spaced apart and arranged so as to define first and second basis states of a quantum bit, gate electrodes for preparing said first state as a superposition of said first and second basis states and gate electrodes for controlling coupling between said first and second quantum dots so as to transform said first state into said second state.
The first basis state may be defined by a first given charge distribution across said first and second quantum dots and the second basis state may be defined by a second given charge distribution across said first and second quantum dots.
The first basis state may be defined by a given amount of excess charge on said first quantum dot relative to said second quantum dot and the second basis state may be defined by a given amount of excess charge on said second quantum dot with respect to said first quantum dot.
The gate electrodes for controlling coupling between said first and second quantum dots may comprise an electrode for adjusting a tunnel barrier disposed between said first and second quantum dots.
The first and the second quantum dots may be of unequal size.
The quantum computer may comprise a conductive channel region between source and drain regions. The conductive channel region may be substantially planar.
A first portion of the conductive channel region may be configured so as to define a first tunnel barrier and a second portion of the conductive channel region may be configured so as to define a second tunnel barrier. A third portion of the conductive channel region may be configured so as to define a second tunnel barrier. The conductive channel region may comprise a semiconductor, such as silicon-germanium. The semiconductor may be doped with an impurity and the impurity concentration may be at least 1xc3x971019 cmxe2x88x923. The impurity can be an acceptor, such as boron.
The conductive channel region may be isolated by at least one trench.
The first and second quantum dots may be configured so as to exhibit Coulomb blockade.
The quantum computer may comprise a sensor for measuring charge on at least one of said first and second quantum dots or sensors for measuring charge on each of said first and second quantum dots. The sensor for measuring charge may comprise a single-electron electrometer.
According to a second aspect of the present invention there is provided a quantum computer for transforming a first state into a second state comprising an array of elements, each element of the array comprising: a first quantum dot, a second quantum dot, said first and second quantum dots being spaced apart and arranged so as to define first and second basis states of a quantum bit, gate electrodes for preparing a quantum bit state as a superposition of said first and second basis states, said elements being arranged so as to cause entanglement of the quantum bits of said elements of said array, gate electrodes for preparing said first state as an entangled superposition of quantum bit states and gate electrodes for controlling coupling between first and second quantum dots of at least one element so as to transform said first state into said second state.
According to the present invention there is also provided apparatus including a quantum computer and a source for providing a time dependant electric field to said quantum computer. The source can be a laser, a gate electrode or a source which generates microwaves.
According to the present invention there is also provided apparatus including a quantum computer and control circuitry for controlling said gate electrodes.
According to the present invention there is also provided apparatus including a quantum computer and a refrigerator for cooling said quantum computer.
According to a third aspect of the present invention there is provided a method of operating a quantum computer comprising a first quantum dot, a second quantum dot, said first and second quantum dots being spaced apart and arranged so as to define first and second basis states, the method comprising preparing a first state as a superposition of said first and second basis states and controlling coupling between said first and second quantum dots so as to transform said first state into a second state.
The controlling of the coupling between said first and second quantum dots may comprise lowering a tunnel junction disposed between said first and second quantum dots for a predetermined period of time.
The method may comprise providing an excitation so as to cause Rabi oscillations between said first and second states.
According to a fifth aspect of the present invention there is provided a quantum computer for transforming a first state into a second state comprising a structure for defining a first quantum dot, a structure for defining a second quantum dot, said structures for defining said first and second quantum dots being spaced apart and arranged so as to define first and second basis states of a quantum bit, gate electrodes for preparing said first state as a superposition of said first and second basis states and gate electrodes for controlling coupling between said first and second quantum dots so as to transform said first state into said second state.
According to a fifth aspect of the present invention there is provided an electronic device comprising a channel for charge carriers, a source for providing charge carriers to said channel with a first range of charge carrier energy, said channel comprising a first quantum dot with a first set of energy levels, a second quantum dot with a second set of energy levels having different level spacing from the first set, wherein the first range of charge carrier energy is greater than the spacing between a pair of adjacent energy levels of the first quantum dot and that charge carrier transport through the device only takes place through a one of the first set of energy levels and a one of the second set of energy levels which are energetically aligned.